If $\sqrt{2} = 1.4142$,then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3}) = \ldots \ldots \ldots$

If $x = 2 + \sqrt{3},$ then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}.$

Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.